Numerical solution of fractional order differential equations by extrapolation

被引：140

作者：

Diethelm, K

Walz, G

机构：

[1] Univ Hildesheim, Math Inst, D-31141 Hildesheim, Germany

[2] Univ Mannheim, Dept Math & Comp Sci, D-68131 Mannheim, Germany

来源：

NUMERICAL ALGORITHMS | 1997年 / 16卷 / 3-4期

关键词：

fractional order derivative; fractional order differential equation; quadrature; extrapolation; asymptotic expansion; trapezoidal formula;

D O I：

10.1023/A:1019147432240

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present an extrapolation type algorithm for the numerical solution of fractional order differential equations. It is based on the new result that the sequence of approximate solutions of these equations, computed by means of a recently published algorithm by Diethelm [6], possesses an asymptotic expansion with respect to the stepsize. From this we conclude that the application of extrapolation is justified, and we obtain a very efficient differential equation solver with practically no additional numerical costs. This is also illustrated by a number of numerical examples.

引用

页码：231 / 253

页数：23

共 21 条

[1]

Brass H., 1977, Quadraturverfahren

[2] A GENERAL EXTRAPOLATION ALGORITHM [J].